Marrou first ran for the Alaska House of Representatives in 1982, placing second in a three-way race. He was then elected to the House in 1984.[3] One of twelve Libertarians to be elected to a state legislature, Marrou served for one term, from 1985 to 1987.[1] Running for reelection in 1986, he would lose to Claude E. "Swack" Swackhammer, a former Alaska State Trooper.[4] Marrou left Alaska following his 1986 defeat and moved to Las Vegas, Nevada, where he worked as a real estate broker.[4]

Marrou had most of his campaign staff resign during the summer of 1992, mainly because he was willing to accept a federal campaign subsidy in contradiction to Libertarian Party's non-coercion pledge. Many of them sought to have the Libertarian Party strip him of the nomination because he had unpaid child support, had an arrest warrant in Massachusetts for an outstanding contempt of court charge, claimed to have been married twice when it was in fact four times, was being investigated for campaign improprieties from his time in Alaska, was running up unpaid credit card bills in a campaign PAC's name without their approval, and was habitually months late in making his house payments. The national committee decided to take no action for fear it would call attention to these issues.[14]